1. Lay half of the bacon slices on a large sheet of plastic wrap. Set the skirt steaks on top and cover with the remaining bacon. Wrap and refrigerate overnight, or for 24 hours.
2. Melt 2 tablespoons of the butter in a large skillet. Add the shallots and cook over low heat, stirring, until softened, about 5 minutes. Add all of the mushrooms, season with salt and pepper, cover and cook until they have released their liquid, about 4 minutes. Uncover and cook over moderate heat until the mushrooms are browned on the bottom, about 3 minutes. Stir and cook for 4 minutes longer. Add the remaining 1 tablespoon of butter and cook, stirring, for 1 minute. Season with salt and pepper and transfer to a saucepan.
3. Remove the bacon slices from the steak and save for another use. Heat 1/2 tablespoon of the oil in each of 2 large skillets. Add 2 steaks to each skillet and cook over moderately high heat until browned on the bottom, about 3 minutes. Turn the steaks and cook until medium rare, about 3 minutes longer. Transfer the steaks to a carving board and let rest for 5 minutes.
4. Gently reheat the mushrooms and stir in the parsley. Thinly slice the steaks across the grain and arrange on plates. Top with the mushrooms and serve.